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Re: Cable around the Equator
Posted:
Nov 5, 1996 1:56 PM


Yes it is correct. Try this similar one and see if it passes the sanity test. This comes from CPM geometry.
A 1000 foot metal bridge is constructed with a hinge in the center to allow for heat expansion. When it is very hot, the bridge expands by one foot, thus raising it up in the center at the hinge.
Using Pythagorean theorem, you should be able to tell me how high the hinge rises when it is hot. I believe that this answer will also surprise you, perhaps even more than the previous example.
domroy
At 12:23 11/5/96 0800, you wrote: >What also challenges your sanity is that it matters not the size of the >original sphere....it could be the size of the earth as in the original, >or the moon, or a beach ball or even the size of a golf ball. My kids >have a tough time accepting the "real mathematics" as the correct (sane) >answer. They initially don't believe their numbers. But we work at it. > >Art Mabbott >****************************************************************************** From the Net: mabbotta@belnet.bellevue.k12.wa.us From the Web: http://belnet.bellevue.k12.wa.us/~mabbotta > __ _______ >   /  Newport High School >  `'*  4333 128th Ave. S.E. >   Bellevue, WA 98006 > _  (206) 4556136 (Work) > \__________ (206) 7465449 (FAX) > (206) 8836087 (Home) > >On Tue, 5 Nov 1996, Juan Miguel Vilar wrote: > >> Not only was his math impeccable, it was also correct! I think that >> it passes correctly the sanity check, where is the problem? >> >> Juan Miguel Vilar >> >> >> On 5 Nov 1996, mfr1 wrote: >> >> > How can adding 50' of slack to the cable spread evenly around the equator >> > add 8' at each point? Your math was impeccable but your answer does not >> > pass the sanity check! This is why we must not blindly accept mathematical >> > results. That is the lesson to be learned from this geometry problem. >> > >> > lipp@educ.umass.edu wrote in article >> > <Pine.PMDF.3.91.961104130200.557939369A100000@oitvms.oit.umass.edu>... >> > > >> > > >> > > On Mon, 4 Nov 1996, mfr1 wrote: >> > > >> > > > Ma Bell wants to place a telephone cable around the equator. She adds >> > 50 >> > > > feet to the length of the cable beyond what is required. This slack in >> > the >> > > > cable allows the cable to be strung up above the ground. How high up >> > from >> > > > the surface of the earth will the cable stand? You can assume that the >> > > > earth is a perfect sphere. >> > > > >> > > > In your mind, run a sanity check on your answer to see if it makes >> > sense. >> > > > >> > > Surprisingly, you will be able to walk under the cble easilty. Since the >> > >> > > circumference of a circle is C = 2piR, each increase in R obf 1 foot >> > > increases the circumference by 2pi feet. since the cable has been >> > > increased by 50 feet the radius of the cablecircle will be increased by >> > > 50/2pi or about 8 feet! >> > > >> > > Alan Lipp >> > > >> > >> >> >



